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**Find the median of the following data (1-8) 83, 37, 70, 29, 45, 63, 41, 70, 34, 54**

Arranging the data in ascending order, we have:

29, 34, 37, 41, 45, 54, 63, 70, 70, 83

Here, the number of observations, *n* = 10 (Even).

Hence, the median of the given data is 49.5.

**Find the median of the following data (1-8) 133, 73, 89, 108, 94, 104, 94, 85, 100, 120**

Arranging the data in ascending order, we have:

73, 85, 89, 94, 94, 100, 104, 108, 120, 133.

Here, the number of observations *n* = 10 (Even).

Hence, the median of the given data is 97.

**Find the median of the following data (1-8) 31, 38, 27, 28, 36, 25, 35, 40**

Arranging the data in ascending order, we have:

25,27, 28, 31, 35, 36, 38, 40

Here, the number of observations *n* = 8 (Even).

Hence, the median of the given data is 33.

**Find the median of the following data (1-8) 15, 6, 16, 8, 22, 21, 9, 18, 25**

Arranging the data in ascending order, we have:

6, 8, 9, 15,16,18, 21, 22, 25

Here, the number of observations *n* = 9 (Odd).

â‡’Median=Value of observati5on i.e , value of the 5th observation = 16

Hence, the median of the given data is 16

**Find the median of the following data (1-8) 41, 43, 127, 99, 71, 92, 71, 58, 57**

Arranging the given data in ascending order, we have:

41, 43, 57, 58, 71,71, 92, 99, 127

Here, *n* = 9, which is odd.

âˆ´ Median = Value of observation, i.e., the 5^{th} observation = 71.

**Find the median of the following data (1-8) 25, 34, 31, 23, 22, 26, 35, 29, 20, 32**

Arranging the given data in ascending order, we have:

20, 22, 23, 25, 26, 29, 31, 32, 34, 35

Here, *n* = 10, which is even.

Hence, the median is 27.5 for the given data.

**Find the median of the following data (1-8) 12, 17, 3, 14, 5, 8, 7, 15**

Arranging the given data in ascending order, we have:

3,5,7,8,12,14,15,17

Here, *n* = 8, which is even.

Hence, the median of the given data is 10.

**Find the median of the following data (1-8) 92, 35, 67, 85, 72, 81, 56, 51, 42, 69**

Arranging the given data in ascending order, we have:

35, 42, 51, 56, 67, 69, 72, 81, 85, 92

Here, *n* = 10, which is even.

Hence, the median of the given data is 68.

**Numbers 50, 42, 35, 2 x + 10, 2x âˆ’ 8, 12, 11, 8, 6 are written in descending order and their median is 25, find x.**

Here, the number of observations *n* is 9. Since *n* is odd , the median is the observation, i.e. the 5^{th} observation.

As the numbers are arranged in the descending order, we therefore observe from the last.

Median = 5^{th} observation.

â‡’ 25 = 2*x* -8

â‡’ 2*x* = 25 +8

â‡’ 2*x* = 33

â‡’*x* = 33/2

â‡’*x* = 16.5

Hence, *x* = 16.5.

**Find the median of the following observations : 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?**

Arranging the given data in ascending order, we have:

33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

Here, the number of observations *n* is 11 (odd).

Since the number of observations is odd, therefore,

Median = Value of observation = Value of the 6^{th} observation = 58.

Hence, median = 58.

If 92 is replaced by 99 and 41 by 43, then the new observations arranged in ascending order are:

33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99.

âˆ´ New median = Value of the 6^{th} observation = 58.

**Find the median of the following data : 41, 43, 127, 99, 61, 92, 71, 58, 57, If 58 is replaced by 85, what will be the new median?**

Arranging the given data in ascending order, we have:

41, 43, 57, 58, 61, 71, 92, 99,127

Here, the number of observations, *n,* is 9(odd).

âˆ´ Median = Value of observation = Value of the 5^{th} observation = 61.

Hence, the median = 61.

If 58 is replaced by 85 , then the new observations arranged in ascending order are:

41, 43, 57, 61, 71, 85, 92, 99,12 .

âˆ´ New median = Value of the 5^{th} observation = 71.

**The weights (in kg) of 15 students are : 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.**

Arranging the given data in ascending order, we have:

27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45.

Here, the number of observations *n* is 15(odd).

Since the number of observations is odd, therefore,

Median = Value of observation = Value of the 8^{th} observation = 35.

Hence, median = 35 kg.

If 44 kg is replaced by 46 kg and 27 kg by 25 kg , then the new observations arranged in ascending order are:

25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46.

âˆ´ New median = Value of the 8^{th} observation = 35 kg.

**The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x : 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95**

Here, the number of observations *n* is 10. Since *n* is even,

â‡’63 = x+1

â‡’x = 63âˆ’1 = 62.

Hence, *x* = 62.